The Tier-1 ISPs have been considered the Internet's backbone since the dawn of the modern Internet 30 years ago, as they guarantee global reachability. However, their influence and importance are waning as Internet flattening decreases the demand for transit services and increases the importance of private interconnections. Conversely, major cloud providers - Amazon, Google, IBM, and Microsoft - are gaining in importance as more services are hosted on their infrastructures. They ardently support Internet flattening and are rapidly expanding their global footprints, which enables them to bypass the Tier-1 ISPs and other large transit providers to reach many destinations. In this paper we seek to quantify the extent to which the cloud providers' can bypass the Tier-1 ISPs and other large transit providers. We conduct comprehensive measurements to identify the neighbor networks of the major cloud providers and combine them with AS relationship inferences to model the Internet's AS-level topology to calculate a new metric, hierarchy-free reachability, which characterizes the reachability a network can achieve without traversing the networks of the Tier-1 and Tier-2 ISPs. We show that the cloud providers are able to reach over 76% of the Internet without traversing the Tier-1 and Tier-2 ISPs, more than virtually every other network.